Microelectrode Measurements of Local
Mass Transport Rates in
Heterogeneous Biofilms
Kjetil Rasmussen,* Zbigniew Lewandowski
Center for Biofilm Engineering, 409 Cobleigh Hall, P.O. Box 173980,
Montana State University-Bozeman, Bozeman, Montana 59717-3980;
telephone: 406-994-5915; fax: 406-994-6098; e-mail: ZL@erc.montana.edu
Received 14 February 1997; accepted 2 December 1997
Abstract: Microelectrodes were used to measure oxygen
profiles and local mass transfer coefficient profiles in bio-
film clusters and interstitial voids. Both profiles were
measured at the same location in the biofilm. From the
oxygen profile, the effective diffusive boundary layer
thickness (DBL) was determined. The local mass transfer
coefficient profiles provided information about the na-
ture of mass transport near and within the biofilm. All
profiles were measured at three different average flow
velocities, 0.62, 1.53, and 2.60 cm sec−1, to determine the
influence of flow velocity on mass transport. Convective
mass transport was active near the biofilm/liquid inter-
face and in the upper layers of the biofilm, independent
of biofilm thickness and flow velocity. The DBL varied
strongly between locations for the same flow velocities.
Oxygen and local mass transfer coefficient profiles col-
lected through a 70 µm thick cluster revealed that a clus-
ter of that thickness did not present any significant mass
transport resistance. In a 350 µm thick biofilm cluster,
however, the local mass transfer coefficient decreased
gradually to very low values near the substratum. This
was hypothetically attributed to the decreasing effective
diffusivity in deeper layers of biofilms. Interstitial voids
between clusters did not seem to influence the local
mass transfer coefficients significantly for flow velocities
of 1.53 and 2.60 cm sec−1. At a flow velocity of 0.62 cm
sec−1, interstitial voids visibly decreased the local mass
transfer coefficient near the bottom. © 1998 John Wiley &
Sons, Inc. Biotechnol Bioeng 59: 302–309, 1998.
Keywords: biofilms; microelectrodes; local mass transfer
coefficient; effective diffusivity
INTRODUCTION
Recent studies of biofilm architecture strongly influence our
concepts of mass transport mechanisms within biofilms. Im-
ages of living biofilms, obtained using scanning confocal
laser microscopy (SCLM), show that biofilms form cellular
clusters separated by interstitial voids filled with either wa-
ter or biopolymers (Keevil and Walker, 1992; Korber et al.,
1994; Lawrence et al., 1991; Wolfaardt et al., 1994). It is
well known that the nonuniform distribution of biomass in
biofilms may influence the mass transport mechanism. Re-
ports of such influences were published even before we
fully realized the importance of biofilm architecture. The
study of the nature of oxygen distribution within structurally
heterogeneous biofilms clearly demonstrated the impor-
tance of biofilm architecture to oxygen transport (De Beer et
al., 1994a). Siegrist and Gujer (1985) observed an increased
average diffusion coefficient with increasing biofilm thick-
ness and hypothesized that this occurs as a result of irregu-
larities of thick biofilms penetrating the boundary layer and
causing eddy diffusion. A similar mechanism may explain
the observations reported by Larsen and Harremoe¨s (1994)
and Horn and Hempel (1995) who found the oxygen diffu-
sion coefficient within a biofilm to be higher than in pure
water. The concept of structurally heterogeneous biofilms
constitutes an intellectual platform to accommodate these
observations, which would otherwise be difficult to inter-
pret. At the recent meeting of the International Association
on Water Quality (IAWQ) Specialist Group on Biofilm Sys-
tems in Leeuwenhorst, the Netherlands, biofilm heteroge-
neity was informally defined as ‘‘spatial differences in any
parameter we think is important’’ (Bishop and Rittmann,
1995).
Despite the awareness of biofilm heterogeneity, there is
no clear consensus on what causes it, or of how the hetero-
geneity influences biofilm processes. Van Loosdrecht et al.
(1995) discussed the influence of substrate loading rate,
shear, and growth rate on the biofilm structure. Some quali-
tative opinions of how the process parameters influence
biofilm structure have been established among biofilm re-
searchers. For example, a high shear rate tends to increase
biofilm density and mechanical stability. Higher substrate
loadings and the presence of fast growing microorganisms
both result in thicker, ragged biofilms. Some researchers
initiated quantification of parameters influencing structural
heterogeneity. Zhang and Bishop (1994a,b) determined the
densities, porosities, specific surface areas, and mean pore
radii of biofilms. In addition, they determined the distribu-
tion of the tortuosity factor and the ratio of the effective
diffusivity in a biofilm to diffusivity in the bulk solution. Fu
* Present address: Department of Biotechnology, The Norwegian Uni-
versity of Science and Technology, N-7034, Trondheim, Norway.
Correspondence to: Zbigniew Lewandowski
Contract grant sponsors: National Science Foundation; Montana State
University
Contract grant numbers: Cooperative Agreement EEC-8907039
© 1998 John Wiley & Sons, Inc. CCC 0006-3592/98/030302-08
et al. (1994) estimated the effective diffusivity in different
layers of a biofilm using a dissolved oxygen microelectrode.
Hermanowicz et al. (1995) used SCLM images to estimate
the fractal dimension and biofilm morphology.
Biofilm reactivity is controlled by the rate of substrate
consumption and by the rate of mass transport. Mass trans-
port in biofilms is traditionally described using the film
theory which assumes the presence of a fictitious film of
fluid in laminar flow next to the boundary. The fictitious
film provides the same amount of mass transfer resistance
as actually exists in the flowing fluid. Hence, all mass trans-
fer resistance exists in this fictitious film in which mass
transport only occurs as molecular diffusion (Welty et al.,
1976). Revsbech and Jørgensen (1986) refer to this film as
the effective diffusive boundary layer (DBL). Lewandowski
(1994) developed a method for calculating the thickness of
the DBL from substrate concentration profiles. According to
the film theory, the flux of substrate to a biofilm can be
described using finite differences in Fick’s diffusion equa-
tion:
J = D
DC
DBL (1)
where J is flux (mol m−2 sec−1), D is the diffusion coeffi-
cient of the substrate in stagnant water (m2 sec−1), DC is the
difference in the solute concentration (mol m−3) between the
bulk liquid and at the reacting surface, and DBL is the
thickness of the effective diffusive boundary layer (m).
From this definition, the mass transfer coefficient is the ratio
of the diffusion coefficient to the thickness of the DBL, k 4
D/DBL. The value of the mass transfer coefficient depends
on many factors, with hydrodynamics being the most sig-
nificant, because flow velocity influences the thickness of
the DBL. The higher the flow velocity, the thinner the DBL.
Experiments have demonstrated the true nature of hydro-
dynamics near biofilms. Lewandowski et al. (1993) used
Nuclear Magnetic Resonance Imaging (NMRI) to show that
water was moving in the space occupied by the biofilm.
This study was followed by quantification of the intra-
biofilm flow using a combination of particle tracking and
SCLM. De Beer et al. (1994b) and Stoodley et al. (1994)
determined the flow velocity profiles in voids and channels.
The flow in biofilms occurs in two flow fields—one inside
and one outside the biofilm (Lewandowski et al., 1995). The
external and internal flow fields influence each other in a
complex way. These studies indicate that direct application
of the film theory may be confounding and demonstrate that
the mass transport in biofilms is affected by convection to a
much larger extent than previously suspected. Because of
complex hydrodynamics, the intensity of convective mass
transport in biofilms is difficult to quantify. To address this
problem, Yang and Lewandowski (1995) developed a mi-
crotechnique to evaluate the local mass transfer coefficient
in biofilms by measuring the limiting current drawn from a
mobile microelectrode. The limiting current technique,
based on the reduction of dissolved electroactive species at
a cathodically polarized electrode, is often used to deter-
mine mass transfer rates to surfaces (Dawson and Trass,
1972; Hanratty, 1991; Juhasz and Deen, 1993). The concept
of local mass transport coefficient introduced by Yang and
Lewandowski (1995) results directly from the limiting cur-
rent technique with the exception of using a mobile elec-
trode, instead of a stationary one, to measure the limiting
current. The flux of electroactive species to a polarized
electrode is:
J 4 k (CO − CS) (2)
where CO is the concentration of the reacting species in the
bulk, and CS is the concentration of the reacting species at
the surface of the microelectrode. The flux of electroactive
species may be calculated from the polarization current:
J =
I
nAF (3)
where I is the polarization current, A is surface area of the
electrode, and n is number of moles of electrons transferred
in the electrode reaction. Equations (2) and (3), when solved
for the mass transfer coefficient, yield:
k =
I
nAF ~CO − CS!
(4)
During the local mass transfer coefficient measurements,
the polarization potential of the electrode is fixed at a po-
tential which causes the concentration of electroactive spe-
cies at the electrode surface (CS) to be zero—a state referred
to as the limiting current condition. This situation is easily
recognized, because a further increase in the polarization
potential does not increase the current (within limits, of
course). Having CS 4 0 simplifies equation (4) and allows
for the calculation of the mass transport coefficient (k) from
the measured parameters. The calculated mass transfer co-
efficient is called the local mass transport coefficient—the
mass transport coefficient which reflects the resistance of
mass transport to the tip of the microelectrode. The local
mass transport coefficient should not be confused with the
overall mass transport coefficient which controls the mass
transport rate to the biofilm surface through the DBL [see
eq. (1)]. The latter (overall) mass transport coefficient can
be evaluated from the substrate concentration profiles mea-
sured by substrate specific microelectrodes. The local mass
transfer coefficient reflects the mass transfer resistance
in the immediate vicinity of the electrode tip, and thus is
sensitive to the local hydrodynamics, local effective diffu-
sivity (biofilm density), and biofilm architecture. Yang and
Lewandowski (1995) reported that the local mass transfer
coefficient varied both horizontally and vertically within
biofilms.
To study the nature of mass transport near and within
biofilms, we combined the measurements of the local mass
transfer coefficients with the measurements of local dis-
solved oxygen concentrations. A bacterial biofilm com-
RASMUSSEN AND LEWANDOWSKI: MASS TRANSPORT IN BIOFILMS 303
posed of aerobic microorganisms was grown in an open
channel flow reactor. Profiles of dissolved oxygen were
measured at different flow velocities, through the cell clus-
ters, and through the interstitial voids. Subsequently, the
growth medium was replaced with a ferricyanide solution,
the local mass transfer coefficient profiles were measured at
the same locations. Superimposing the two profiles indi-
cates the effects of biofilm architecture and hydrodynamics
on the rate of oxygen transport.
MATERIALS AND METHODS
The experimental set-up was similar to that described by
Yang and Lewandowski (1995). The biofilm was grown in
an open channel reactor 40 mm wide by 500 mm long made
of polycarbonate. A concentrated nutrient solution and fil-
tered tap water (PAC-filter, Model CBC-10, Cole-Parmer
Instr. Co., Chicago, IL) was aerated in a mixing chamber
before it was recycled through the reactor by a peristaltic
pump (Cole-Parmer Instr. Co., Chicago, IL). The influent
nutrient solution from the mixing chamber consisted of
KH2PO4 (0.69 mM), K2HPO4 (1.5 mM), (NH4)2SO4 (0.079
mM), MgSO4*7H2O (0.013 mM), and yeast extract (0.031 g
L−1). The total reactor volume was 420 mL, and the hy-
draulic retention time was only 4 min and 30 sec to avoid
suspended growth. One-mL portions of stock cultures of
Pseudomonas aeruginosa (7.7 × 109 CFU/mL), Pseudomo-
nas fluorescens (4.8 × 1010 CFU/mL), and Klebsiella pneu-
moniae (7.2 × 1010 CFU/mL) were used to inoculate the
reactor. After inoculation, the reactor was operated in a
batch mode for 24 h, followed by continuous flow mode for
5 d at room temperature. During the period of continuous
flow, the reactor was tilted to obtain a shallow water depth,
and hence, a high volumetric flow velocity set to 17 cm
sec−1. The high flow velocity during the growth phase was
used to obtain biofilms of high density which were strongly
attached to the bottom. This was necessary to avoid detach-
ment or change of structure during the experiments in which
a range of different microelectrodes, flow velocities, and
solutions were used. After the biofilm was established, the
reactor was positioned horizontally and the measurements
were conducted at flow velocities of 0.62, 1.53, and 2.60 cm
sec−1.
Oxygen profiles were measured by a combined dissolved
oxygen and reference microelectrode. The electrode was
constructed as described by Revsbech (1989b). The oxygen
sensor consisted of a 100 mm 99.99% pure platinum wire
(California Wire Company, Grover Beach, CA), etched on
one end to a diameter of 5 mm and covered by Schott 8533
glass (Schott Glaswerke, F.R.G.). The tip was exposed with
a heating loop, and then goldplated. A 0.5 mm diameter,
99.99% pure silver wire, coated with an AgCl layer, was
used as the silver/silver chloride reference electrode. The
guard cathode was made from a 100 mm diameter, 99.99%
pure silver wire (California Fine Wire Company, Grover
Beach, CA). It was then fixed in a thin glass capillary.
Approximately 1.5 cm of the wire was sticking out of the
capillary on both ends. The oxygen sensor, the reference
electrode, and the guard cathode were mounted inside a 53⁄4
inch long Pasteur Pipet (Fisher Scientific, Pittsburgh, PA)
tapered to 10 mm at one end. A 10 mm thick uncured sili-
cone membrane was applied on the tapered tip. The shaft
was filled with electrolyte containing K2CO3 (0.3M),
KHCO3 (0.2M), and KCl (1.0M), then sealed with epoxy.
Microelectrodes to measure profiles of the local mass
transfer coefficient were constructed following the proce-
dure of Yang and Lewandowski (1995). Microelectrodes
were made of 100 mm (pure TC grade) platinum wire (Cali-
fornia Wire Company, Grover Beach, CA), with the tips
etched electrochemically in 2M KCN solution to a diameter
of less than 1 mm. The glass capillary was positioned in a
Micro Electrode Puller (Stoelting Co., Wooddale, IL), while
the tip of the wire was positioned 1 to 1.5 cm above the
heating coil. Heat was gradually increased until the glass
around the platinum wire melted and adhered to the wire
while the entire capillary dropped down and cooled in the
air. The tip of the wire was then exposed by grinding on a
rotating diamond wheel (Model EG-4, Narishige Co, To-
kyo, Japan). Tip diameter was measured microscopically to
calculate the surface area of the electrode. The counter-
reference electrode was a commercial calomel electrode
(Model 13-620-51, Fisher Scientific, Pittsburgh, PA).
A micromanipulator (Model M3301L, World Precision
Instruments, New Haven, CT) was used to move the micro-
electrodes. It was equipped with a stepper motor (Model
18503, Oriel, Stratford, CT) and manipulated by a computer
controller (Model 20010, Oriel, Stratford, CT). The elec-
trodes were moved from the bulk liquid down through the
biofilm in 10 mm increments. The measured signal was
directed to a computer containing a data acquisition system.
Dissolved oxygen profiles were measured first. After the
measurement, the nutrient solution was replaced by a solu-
tion of the electroactive species. Local mass transfer coef-
ficient profiles were measured at the same locations as the
dissolved oxygen profiles. The reactor was fixed to an X-Y
micropositioner stage (Model CTC-462-2S, MicroKinetics,
Laguna Hills, CA). The stage was computer controlled
through a controller (Model CTC-283-3, MicroKinetics, La-
guna Hills, CA). A computer equipped with custom-made
software was used to control the stage movement. Before
each set of measurements, a reference point was selected on
the substratum using an inverted microscope (Model CK-2,
Olympus, Japan), and the DO-probe was positioned directly
above this point with a precision of 10 mm. The reactor
departure from the reference point in the X and Y directions
was then recorded. At each location, DO-profiles were col-
lected for different volumetric flow velocities. The inverted
microscope was also used to locate the tip of the microelec-
trode and to observe when the electrode reached the sub-
stratum. Before the local mass transfer coefficient measure-
ments were taken, the reactor was drained, and a solution
containing 25 mM potassium ferricyanide and 0.5M potas-
sium chloride as supporting electrolyte was added. It was
recycled through the reactor for 30 min to obtain a constant
304 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 59, NO. 3, AUGUST 5, 1998
ferricyanide concentration throughout the biofilm. The ref-
erence point was again found under the microscope, and the
local mass transfer coefficient electrode was positioned
above it with a precision of 10 mm. The reactor was then
moved by the X-Y stage to the same locations at which the
DO profiles were collected, and local mass transfer coeffi-
cient profiles were measured for the same flow velocities.
The data acquisition system (Model CIO-DAS08PGL,
Computer Boards, Inc., Mansfield, MA) collected current
data from the Picoammeter/DC Voltage Source (Hewlett
Packard 4140B). On the computer monitor, the vertical pro-
files of oxygen or local mass transfer coefficient were dis-
played in real time. At each step, 22 current readings were
collected at a frequency of 1 KHz. The highest and lowest
were rejected and a standard deviation was calculated for
the remaining 20 readings. If the deviation was higher than
5%, the measurement at that location was repeated.
During the local mass transfer coefficient measurements,
a potential of −0.8 volts was applied between the micro-
electrode and the reference electrode. As a result, ferricya-
nide diffused to the tip of the electrode and was reduced to
ferrocyanide:
Fe(CN)63− + e− → Fe(CN)64− (5)
The current drawn by the electrode was proportional to the
local mass transfer coefficient:
k 4 I/nAFC0 (6)
where k is the local mass transfer coefficient, I is the lim-
iting current, n is the number of electrons transferred in the
reaction [one from eq. (5)], A is the sensing area of the
microelectrode, F is Faraday’s constant, and C0 is the fer-
ricyanide concentration in the bulk solution.
Lewandowski et al. (1993, 1994) demonstrated that the
shape of oxygen profiles in biofilms may be described by
the following equation:
C − Cs
Cb − Cs
= 1 − exp @−B~X − Xs!# (7)
where C is the local substrate concentration, Cs is the sub-
strate concentration at the biofilm surface, Cb is the bulk
substrate concentration, B is an experimental coefficient, X
is the distance from the substratum to the biofilm surface
(biofilm thickness), and (X − Xs) is the distance measured
from the biofilm surface toward the bulk liquid phase. This
equation can be linearized to conveniently calculate the co-
efficient B from experimental data:
Ln S1 − C − CsCb − CsD = −B ~X − Xs! (8)
We used 1/B as a measure of the DBL thickness (Lewan-
dowski et al., 1993).
RESULTS AND DISCUSSION
The biofilm was grown at a flow velocity of 17 cm sec−1
(Reynolds number 1000). The reactor was tilted during the
growth cycle to ensure this high flow velocity. Our experi-
ence indicates that biofilms grown at higher flow velocities
are more rigid and less susceptible to sloughing. The biofilm
did not have the fluffy characteristics of biofilms grown at
lower flow velocities, but instead, it consisted of clusters of
different sizes separated by voids and channels. Before the
measurements were taken, the reactor was leveled and the
flow velocity adjusted. Three average flow velocities were
used: 0.62, 1.53, and 2.60 cm sec−1, corresponding to Reyn-
olds numbers of 100, 300, and 600, respectively. To provide
a baseline for mass transport measurements, profiles of local
mass transfer coefficient were measured at the same flow
velocities in a sterile reactor. As shown in Figure 1, the flow
velocity did not have a significant impact on the local mass
transfer coefficient in the bulk liquid under those condi-
tions. The variations noted in mass transfer coefficients
were between 0.00030 and 0.00034 m sec−1. In general, the
mass transfer coefficient remained constant until the elec-
trode was 15 mm from the substratum. From this point, we
measured a sudden drop in local mass transfer coefficient to
less than 50% of its value in the bulk. Although the mea-
surement at the wall could not be performed because of
technical difficulties, the shapes of the profiles in Figure 1
suggest that the mass transfer coefficient approaches zero at
the wall, which corresponds well with the results reported
by Yang and Lewandowski (1995). This effect was ex-
pected based upon the fact that the flow velocity near the
surface decreases to zero, with the consequence that the
convective mass transport rate transport of ferricyanide is
restricted by the wall.
Profiles of dissolved oxygen and local mass transfer co-
Figure 1. Local mass transfer coefficient profiles collected in a sterile
reactor at three average flow velocities; 0.62, 1.53, and 2.60 cm sec−1. The
magnitude of the local mass transfer coefficient remained constant until 15
mm from the substratum. At this point, the wall effect caused a sudden drop
in the local mass transfer coefficient.
RASMUSSEN AND LEWANDOWSKI: MASS TRANSPORT IN BIOFILMS 305
efficients measured in the presence of the biofilm are shown
in Figures 2, 3, and 4. The profiles in Figure 2 were col-
lected at a selected location through a thin cluster, approxi-
mately 70 microns thick. When flow velocity was increased
from 0.62 cm sec−1 to 1.53 cm sec−1, the DBL thickness
decreased from 370 to 60 mm. The oxygen concentration in
the bulk solution was close to 6 mg L−1 and was depleted
inside the biofilm at the lower flow velocity. It is customary
to normalize the limiting current when comparing mass
transfer rates (Gao et al., 1995; Macpherson et al., 1994).
Figure 3. Profiles of oxygen and local mass transfer coefficient through
an interstitial void (j Dissolved oxygen, s Local mass transfer coeffi-
cient). The solid vertical line represents the approximate position of the
biofilm surface. Profiles of dissolved oxygen and local mass transfer co-
efficient were collected at flow velocities of (A) 0.62 cm sec−1, (B) 1.53 cm
sec−1, and (C) 2.60 cm sec−1. The measurements were done in an intersti-
tial void, 200 mm thick. The flow velocity had a significant influence on
both profiles. A 10–20% reduction of the local mass transfer coefficient
was observed through the mass boundary layer. k/kmax reached a value of
0.8–0.9 at the level of the biofilm surface, and decreased to less than 0.4
near the substratum.
Figure 2. Profiles of oxygen and local mass transfer coefficient through
a thin biofilm cluster. (j Dissolved oxygen, s Local mass transfer coef-
ficient). The vertical line marks the observed thickness of the biofilm.
Profiles of dissolved oxygen and local mass transfer coefficient were col-
lected at flow velocities of (A) 0.62 cm sec−1 and (B) 1.53 cm sec−1. At
distances less than 30 mm, the wall effect caused the local mass transport
coefficient to decrease. The biofilm thickness was 70 mm in this location.
k/kmax was only slightly affected by the presence of the biofilm until a
distance less than 30 mm from the substratum. This is simlar to what is
presented in Figure 1 for a sterile reactor.
306 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 59, NO. 3, AUGUST 5, 1998
We normalized the limiting current by dividing each read-
out by the highest current measured for each profile (re-
flecting the local mass transfer coefficient in bulk liquid).
The results indicate that the local mass transfer coefficient
near the biofilm surface was approximately 90% of its value
in the bulk. A rapid decrease in the local mass transfer
coefficient (k/kmax 4 0.5) was monitored at a distance less
than 30 mm from the substratum, which was probably
caused by the presence of the wall (see Fig. 1). These results
indicate that convection was active both inside and outside
the biofilm.
The profiles presented in Figure 3 were measured in a
void between two clusters approximately 200 mm thick. The
bulk flow velocity was expected to significantly influence
the oxygen concentration at this location. At a flow velocity
of 0.62 cm sec−1, the entire interstitial void was depleted of
oxygen, as shown in Figure 3A. By increasing the flow
velocity to 2.60 cm sec−1 (Fig. 3C), the void became fully
penetrated, with an oxygen concentration at the bottom
greater than 1 mg L−1. The oxygen concentration in the bulk
liquid was approximately 6 mg L−1. For the flow velocities
of 0.62, 1.53, and 2.60 cm sec−1, the DBL thicknesses were
440, 420, and 260 mm, respectively. The local mass transfer
coefficient decreased by 10–20% within the liquid layer,
and continues to decrease further below the biofilm surface.
In particular, it decreased rapidly for the lowest flow veloc-
ity where k/kmax reached a value less than 0.4 near the
substratum. Comparing the graphs of Figures 3B and C with
Figure 3A shows that the extent of local mass transfer co-
efficient reduction through the interstitial void depends on
the flow velocity. The local mass transfer coefficient mea-
sured for the flow velocity of 2.60 cm sec−1 was consis-
tently higher and less uniform than for both 0.62 cm sec−1
and 1.53 cm sec−1.
The results of the oxygen and local mass transfer coeffi-
cient profiles measured across a 350 mm thick cluster are
shown in Figure 4. Increasing the velocity from 0.62 to 2.60
cm sec−1 did not significantly change the oxygen concen-
tration gradient inside the biofilm, thus indicating a dense
and active biofilm. There was a 200 mm thick anaerobic
layer in the lower region of the cluster. For the flow veloc-
ities of 0.62 and 1.53 cm sec−1, the local mass transfer
coefficient at the biofilm surface was k/kmax 4 0.8, and
decreased gradually to values near zero at the substratum.
The DBL thicknesses were 200 and 140 mm for these two
velocities, respectively. For the flow velocity of 2.60 cm
sec−1, k/kmax was between 0.6 and 0.7 at the biofilm surface
and was significantly lower than for the lower flow veloc-
ities. k/kmax again decreased gradually through the biofilm
and reached zero at the substratum. In this case, the DBL
thickness was 140 mm.
Figures 2, 3, and 4 show that the slope of the local mass
transfer coefficient increases with increasing flow velocity.
This effect is more prounounced above the cell clusters than
in the void. This effect was not observed in the clean reactor
(Fig. 1), and the reasons for this are unknown. The results in
Figures 2, 3, and 4 indicate a complex pattern of mass
Figure 4. Profiles of oxygen and local mass transfer coefficient through
a 350 mm thick biofilm cluster (j Dissolved oxygen, s Local mass trans-
fer coefficient). The solid vertical line represents the approximate position
of the biofilm surface. Profiles of dissolved oxygen and local mass transfer
coefficient through microbial clusters were collected at flow velocities of
(A) 0.62 cm sec−1, (B) 1.53 cm sec−1, and (C) 2.60 cm sec−1. The flow
velocity had minimal influence on the shape of both profiles. The local
mass transfer coefficient at the biofilm surface was 80% of its bulk value.
It decreased gradually through the biofilm and reached zero near the sub-
stratum.
RASMUSSEN AND LEWANDOWSKI: MASS TRANSPORT IN BIOFILMS 307
transport inside the biofilm. If cells and extracellular poly-
mers were uniformly distributed throughout a cell cluster,
and no convection occurred, we would expect a constant
local mass transfer coefficient within these aggregates.
However, Figure 4 shows that the local mass transfer coef-
ficient decreases gradually inside a cluster, approaching
zero near the substratum. The local mass transfer coefficient
is a function of the effective diffusivity of ferricyanide and
of the thickness of the boundary layer surrounding the tip of
the microelectrode. A change in either of these two param-
eters will cause a change in the local mass transfer coeffi-
cient. The gradual decrease in the local mass transfer coef-
ficient through the biofilm cluster can be caused by a
gradual increase in the biofilm density. As the density in-
creases, mass transfer resistance increases while the effec-
tive diffusivity, as well as the local mass transfer coeffi-
cient, decrease. It has been reported in the literature that the
density of some biofilms increases towards the substratum.
Zhang and Bishop (1994b) determined that the densities in
the bottom layers of a heterotrophic biofilm were 5–10
times higher than those in the top layers. Fu et al. (1994)
determined the effective diffusivity of oxygen in different
layers of a biofilm, showing that it was 25–90% lower than
the diffusivity of oxygen in water.
Experiments are currently in progress in our lab to verify
the hypothesis that the effective diffusivity decreases to-
wards the bottom of the biofilm. A local mass transfer co-
efficient profile has been measured through a biofilm under
stagnant conditions. The local mass transfer coefficient de-
creased gradually within clusters, approaching zero near the
bottom, similar to the profiles collected in a flow field (Fig.
4). Under stagnant conditions, the thickness of the boundary
layer surrounding the microelectrode tip is constant, and the
only parameter that can cause the reduced local mass trans-
fer coefficient is the effective diffusivity.
Tortuosity and porosity also influence the effective dif-
fusivity. Zhang and Bishop (1994a) reported that for a bio-
film with porosities of 0.84–0.93 in the top layers and 0.58–
0.67 in the bottom layer, the tortuosity factor increased from
1.2 in the top layer to 1.6 in the bottom layer. In the same
biofilm, the ratio of the effective diffusivity to the diffusiv-
ity in the bulk solution decreased from 68–81% in the top
layer and 38–45% in the bottom layer. Zhang and Bishop
(1994a) defined pores as space between clusters. In their
model, the clusters obstructed the transport of substrate
thereby causing tortuosity. The concept of porosity and tor-
tuosity can be applied on a smaller scale to clusters where
cells obstruct the transport of substrate. Substrate transport
to cells in the bottom layer of a biofilm is more likely to
occur around rather than through the cells. Hence, the cells
cause tortuosity. Regions with higher concentrations of cells
will have higher tortuosity and lower porosity than regions
containing less cells. Zhang and Bishop (1994a) calculated
effective diffusivity as De 4 (e/k) Dw where De is the
effective diffusivity, e is the porosity (e < 1), k is the tor-
tuosity factor (k > 1), and Dw is the diffusivity in water.
From this equation, it is evident that if the porosity de-
creases and/or the tortuosity increases towards the bottom of
the biofilm, the effective diffusivity, as well as the local
mass transfer coefficient, will decrease.
Yang and Lewandowski (1995) observed irregular pro-
files of the local mass transfer coefficient inside biofilm
clusters. High peaks were believed to be caused by channels
inside the clusters which facilitated convective flow. They
also observed an increased local mass transfer coefficient
just above the biofilm matrix, which was suggested to occur
as a result of active movement of the biofilm surface. These
two effects were not observed in the experiment detailed in
this article. However, the biofilm for the present experiment
was grown at a much higher flow velocity, v 4 17 cm
sec−1, than that of Yang and Lewandowski (1995), v 4 1.3
cm sec−1. It is well known that biofilms growing at a high
flow velocity are relatively rigid and dense (Christensen and
Characklis, 1990; Van Loosdrecht et al., 1995). Therefore,
it is possible that the secondary heterogeneity monitored by
Yang and Lewandowski (1995) was, in the present case,
either less evident or absent.
Models of biofilms (Atkinson and Davies, 1974; Ritt-
mann and McCarty, 1978; Wanner and Gujer, 1986) assume
the existence of a thin diffusive boundary layer above the
biofilm in which the mass transport is dominated by mo-
lecular diffusion. If this is true, a sudden drop should be
observed in the local mass transfer coefficient when enter-
ing this layer. Results presented in this article indicate that
convective mass transport is active in the entire system
down to the biofilm surface, through the interstitial voids,
thin clusters, and in the upper parts of thick clusters. Clus-
ters of 70 mm and less and interstitial voids between clusters
did not significantly influence the local mass transfer coef-
ficient. The only significant reduction in local mass transfer
coefficient was observed in thick cell clusters.
It is clear now that the mass transport dynamics in bio-
films are much more complex than previously assumed. The
following results summarize our findings: (1) Biofilms are
heterogeneous and consist of discrete cell clusters separated
by interstitial voids; (2) the hydrodynamics in biofilms are
controlled by two flow fields, external and internal; and (3)
the mass transfer coefficient in biofilms does not behave as
predicted by current biofilm models. Although the newly
proposed concept of biofilm structure helps to interpret the
experimental observations, the new data reveal further di-
mensions of complexity. We are becoming aware that it
may not be possible to completely describe mass transport
in biofilms mathematically. Some simplifying assumptions
are, therefore, urgently needed to establish empirical equa-
tions serving purely practical purposes. It is important that
these assumptions are established as a result of experimen-
tation, rather than for computational convenience. Our ob-
servations may contribute to this process.
CONCLUSIONS
The measurements presented in this article were conducted
at flow velocities between 0.5 and 2.6 cm sec−1. For these
308 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 59, NO. 3, AUGUST 5, 1998
flow velocities, and for the specific experimental conditions
employed in our work, we concluded that:
1. Convective mass transport was active near the biofilm/
bulk liquid interfaces and in the upper layers of the bio-
films.
2. Thin biofilms, 70 mm or less, did not cause any signifi-
cant changes in local mass transfer resistance.
3. The void spaces between clusters did not cause any sig-
nificant changes in mass transfer resistance for flow ve-
locities of 1.53 cm sec−1 and higher. For a flow velocity
of 0.62 cm sec−1, the local mass transfer coefficient
within the voids decreased gradually towards the bottom.
4. The local mass transfer coefficients in biofilm clusters
350 mm thick and more decreased gradually, approach-
ing zero near the substratum. The decreased local mass
transfer coefficient was likely a result of decreased ef-
fective diffusivity within the biofilm. It is possible that
this decrease in effective diffusivity was due to an in-
crease in the biofilm density near the bottom.
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